Problem: If $x \diamond y = 4x^{2}-y^{2}$ and $x \triangleleft y = 2x-5$, find $(1 \diamond 4) \triangleleft 1$.
Answer: First, find $1 \diamond 4$ $ 1 \diamond 4 = 4(1^{2})-4^{2}$ $ \hphantom{1 \diamond 4} = -12$ Now, find $-12 \triangleleft 1$ $ -12 \triangleleft 1 = (2)(-12)-5$ $ \hphantom{-12 \triangleleft 1} = -29$.